Solve a^2=64/276

$$a ^ { 2 } = \frac { 64 } { 276 }$$

Solve for a

$$a=\frac{4\sqrt{69}}{69}\approx 0.481543412$$

$$a=-\frac{4\sqrt{69}}{69}\approx -0.481543412$$

Steps by Finding Square Root

Reduce the fraction \frac{64}{276} to lowest terms by extracting and canceling out 4.

$$a^{2}=\frac{16}{69}$$

Take the square root of both sides of the equation.

$$a=\frac{4\sqrt{69}}{69} a=-\frac{4\sqrt{69}}{69}$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{64}{276} to lowest terms by extracting and canceling out 4.

$$a^{2}=\frac{16}{69}$$

Subtract \frac{16}{69} from both sides.

$$a^{2}-\frac{16}{69}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{16}{69} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{16}{69}\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-\frac{16}{69}\right)}}{2}$$

Multiply -4 times -\frac{16}{69}.

$$a=\frac{0±\sqrt{\frac{64}{69}}}{2}$$

Take the square root of \frac{64}{69}.

$$a=\frac{0±\frac{8\sqrt{69}}{69}}{2}$$

Now solve the equation a=\frac{0±\frac{8\sqrt{69}}{69}}{2} when ± is plus.

$$a=\frac{4\sqrt{69}}{69}$$

Now solve the equation a=\frac{0±\frac{8\sqrt{69}}{69}}{2} when ± is minus.

$$a=-\frac{4\sqrt{69}}{69}$$

The equation is now solved.

$$a=\frac{4\sqrt{69}}{69} a=-\frac{4\sqrt{69}}{69}$$